George Boole

Co­founder of Symbolic Logic

George Boole was born on November 2, 1815, in Lincoln, England. He realized early that the only way out of poverty was to educate himself. He taught himself Latin and Greek and after his father, a shopkeeper, taught him the mathematics he knew, George took over his own education in this subject as well.

At the age of 16, Boole began teaching to help supplement his family’s income. When he was 20 he opened his own school in Lincoln. He continued his education by reading original sources instead of textbooks. He read some of the work of seventeenth­century mathematicians Pierre ­Simon Laplace and Joseph­ Louis Lagrange and wrote his first original papers about differential equations and invariance. In 1839 Boole began to publish his results in The Cambridge Mathematical Journal In 1844 he published a paper that examined the interplay of techniques in distant algebra and calculus and was awarded a medal by the Royal Society for these contributions.

Boole then began to apply the ideas of abstract algebra to logic. He devised a system in which the logical arguments were written as mathematical expressions. Boole separated his system into quantities, symbolized by letters, and the operations on them. For example he represented those things that were x or y but not both as x+y, and those that were both x and y as xy Given this system, he argued in his 1847 publication Mathematical Analysis of Logic that logic is a part of mathematics. As has often happened in the history of mathematics, the same idea was being suggested by someone else at almost the same time. Augusts De Morgan published Formal Logic the same year.

Although Boole was almost entirely self­ educated, the strength of his publications landed him a professorship in mathematics at Queens College, Ireland, in 1849. He continued to work on his symbolic logic and published a more careful exposition of these ideas in the 1854 An Investigation into the Laws of Thought. He studied logic and probability until his death from pneumonia on December 8, 1864, in Ballintemple, Ireland.

George Boole’s Legacy

Boole’s system of formalized, mathematically expressed logic moved the study of logic forward and eventually would have great significance in the development of computer systems in the twentieth century.

More than a century before Boole, GOTTFRIED LEIBNIZ had tried to formalize logic, without success. At the same time as Boole, De Morgan’s work paralleled Boole’s but stopped short of a comprehensive system of formalized logic. Boole provided a system where rules could be applied to algebraic expressions, and the expressions would represent propositions from which to derive logical conclusions. This system, called Boolean algebra, was later refined and applied to probability and set theory. More important, it helped to form the basis of modern symbolic logic, a formal system of logic represented by symbols, which was later refined by Gottlob Frege in 1879 and furthered in BERTRAND RUSSELL’s and Alfred North Whitehead’s Principia Mathematica in 1913.

Perhaps the most important application of Boolean algebra came in the twentieth century with the development of telephone switching systems and digital computers. Boole’s rules are the same as those in a binary system; they can be applied to situations where the values are only 0 and 1, such as a switch that can be either off (0) or on (1), or a test case that can be either false (0) or true (1). This same system, used exclusively in telephone switching and digital computers, has helped to launch a revolution in information processing and communications that will extend into the next century.